Question

The number of degrees of freedom required for description of pure gas are

• A. 1
• B. 2
• C. 0
• D. 3

Hint:

To describe a pure gas, three parameters — pressure, volume, and temperature — are required, giving the system three degrees of freedom.

Answer 1

The Correct Option is D

A pure (single-component) gas is described macroscopically using three variables: pressure, volume, and temperature. Even though these three are interrelated by an equation of state (such as \( PV = nRT \)), all three are conventionally listed as the degrees of freedom needed to characterize the physical state of the gas in this classification.

Therefore, the correct answer is 3.

Answer 2

Another way to approach this is to think about what happens if we tried to describe a pure gas with fewer variables, checking each option for sufficiency.

1. 1: Using only one variable, say temperature, leaves both pressure and volume completely undetermined, so this is insufficient to describe the gas.
2. 2: Using two variables removes some ambiguity, but the classical description of a gas's physical state still lists pressure, volume, and temperature as the three defining coordinates in this framework.
3. 0: Having no variables at all would mean the gas has a single fixed, universal state, which contradicts the fact that a gas can be compressed, heated, or expanded into many different states.
4. 3: Listing pressure, volume, and temperature together gives a complete macroscopic description of a pure gas sample, which is why three is taken as the number of degrees of freedom here.

Checking insufficiency of fewer variables confirms that three state variables are needed.

Therefore, the correct answer is 3.